This tag is for questions seeking external references (books, articles, etc.) about a particular subject. Please do not use this as the only tag for a question.

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0
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1answer
234 views

Reference for proof of “Dedekind's Criterion”?

It was mentioned to me briefly in passing about a criterion for rings of integers, referred to as Dedekind's Criterion. The Criterion essentially said that a ring $\mathbb{Z}[\omega]$ (for ...
2
votes
2answers
140 views

Are there any places to get highly graphical/visual math videos, specifically for calculus?

I love watching National Geographic and Discovery channel pieces on the universe/outer space because they are so visually appealing, but if I had to read about the topics, I wouldn't have much ...
2
votes
2answers
2k views

Book Reference for Calculus and Linear Algebra :: Engineer

I'm almost through with my (Mech.) engineering and am trying to touch some advanced concepts in Computational Science which requires me to study Calculus and Linear Algebra in a more theoretical ...
8
votes
2answers
394 views

What is an element of a rng called which is not the product of any elements?

Let $R$ be a non-unital ring. Let $F:R\times R\longrightarrow R$ be a function given by the formula $F(x,y)=xy.$ Let $r\not\in\operatorname{im}(F).$ Such elements can exists, for example $2\in ...
4
votes
3answers
487 views

What are some recommended books, online sources, and applications (PC or Android platform) for becoming good at math? [closed]

What are some recommended books, online sources, and applications (PC or Android platform) for becoming good at math? I am specifically looking for books, online resources, and apps that will refresh ...
2
votes
0answers
66 views

A reference for “if a signed measure on a product space is nonnegative on rectangles, then it is nonnegative”

I feel that the following corollary of the Monotone Class Theorem should appear somewhere in the literature, but I haven't been able to find it any of the measure theory books that I have checked. ...
1
vote
0answers
52 views

Necessary condition(s) for transforms of Markov diffusion to stay Markov diffusions

I feel it always necessitates a certain amount of work before reaching the conclusion that the transform of a diffusion by a function is not a Markovian diffusion. I was wondering if there were ...
3
votes
1answer
209 views

Can all first order ODEs be made exact?

Elementary differential equations classes usually cover exact differential equations. These are equations of the form: $$M(x,y)+N(x,y)y'=0 \qquad \mathrm{such\;that} \qquad \frac{\partial ...
0
votes
3answers
363 views

Where can i download “What are the chances?:Probability made clear” lectures videos?

I want to learn probability through lectures videos and i would like to know where i can download The Teaching Company videos for the course titled "What are the chances ? :Probability made clear " I ...
5
votes
1answer
289 views

Not in school. Need some help planning my studies post-calculus & intro. abstract algebra.

OK, so I left school (wasn't failing or anything), but I still love math and want to go on with my studies. I want to, first and foremost, cover all the important topics a math education should ...
3
votes
0answers
225 views

Does the concept of predicativity need to be formalized to go beyond Feferman-Schutte ordinal?

Feferman-Schütte ordinal is sometimes said to be: ....first impredicative ordinal, though this is controversial, partly because there is no generally accepted precise definition of "predicative". ...
4
votes
1answer
61 views

L-function at s=5 with D=-4?

I want to know the value of $L(5,-4)$. Recall that $$ L(s,D)=\sum_{n=1}^\infty \left(\frac{D}{n}\right) n^{-s}. $$ I would like a reference with computations of $L(5,D)$, or more generally, of ...
7
votes
0answers
735 views

How to use Hardy and Wright's text and what corresponding exercises/problem books can I do?

I have just started out with Hardy and Wright's An Introduction to the Theory of Numbers today. I find the lack of exercises in the book as a departure from the style of the textbooks we are so ...
7
votes
3answers
1k views

Good Queuing Theory Introductory Textbook

I am an undergraduate student who is going to be taking a queuing theory introductory course next semester, I am wondering what's a good introductory book out there? (my math background is probability ...
19
votes
4answers
812 views

Out-of-print textbooks that should be reprinted

One of the things I'm looking into doing is beginning a Dover-like publishing company for putting out-of-print textbooks back into print in nice, cheap editions for students. So I'd like to ask the ...
27
votes
3answers
1k views

What can we learn about a group by studying its monoid of subsets?

If $G$ is a group, then $M(G)=2^G$ is has a monoid structure when we define $AB$ to be $\{ab|a\in A,b\in B\}$ and $1_{M(G)}=\{1\}$. How much of the structure of $G$ can be recovered by studying the ...
6
votes
0answers
286 views

Potential theory: discrete-time Markov processes

Recently I've found lecture notes on "Analysis on Graphs" where the potential theory methods were used to study discrete-time, time-reversible Markov chains (i.e. the state space is countable). ...
1
vote
2answers
201 views

First order logic and algebraic structures. Reference request.

I have been encountering many results on logic-related properties of algebraic structures such as elementary equivalence, axiomatizability, definability, etc. The problem is that when I see the proof ...
5
votes
1answer
725 views

On the completeness of the generalized Laguerre polynomials

I am trying to prove that the generalized Laguerre polynomials form a basis in the Hilbert space $L^2(\mathbb{R})$. 1. Orthonormality \begin{equation} \int_0^{\infty} ...
3
votes
3answers
731 views

Oldest books on Calculus

What are some of the oldest books available on Calculus? I'm curious to see how the old teaching and explanatory styles compare to modern ones.
2
votes
1answer
98 views

Reference request for Intuitionism

I need to write an essay on Intuitionism for my Philosophy of Science class, and I'm looking for books which cover the following topics: Brouwer's Intuitionism, from both a philosophical and ...
6
votes
2answers
586 views

References about Sierpinski's Theorem regarding Darboux functions

I am writing something about the following two theorems: Every function $f: \Bbb{R} \to \Bbb{R}$ can be written $f=f_1+f_2$ where $f_1,f_2:\Bbb{R} \to \Bbb{R}$ both have the Darboux property. ...
27
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17answers
2k views

Mathematical toys?

Anybody know of "serious" mathematical ornaments or toys like the Gömböc, etc? Already have a rubix and abacus (that's more of a tool though).
3
votes
0answers
160 views

3-manifold theorem reference request or proof

The following is a theorem of which I have great interest in but cannot find anything about on the internet, Every 3-manifold of finite volume comes from identifying sides of some polyhedron I'm ...
1
vote
1answer
73 views

Reference for existence of quotients of modular Jacobians?

In the construction of Galois representations attached to modular forms of weight 2, the representation spaces can be found in Tate modules of certain quotients of Jacobians of modular curves by ...
3
votes
5answers
328 views

Essays on the real line?

Are there any essays on real numbers (in general?). Specifically I want to learn more about: The history of (the system of) numbers; their philosophical significance through history; any good ...
1
vote
0answers
56 views

formulas for exact values of singular values in low dimension?

Are there formulas for the singular values of a real matrix in low dimension, i.e. for a $2 \times 2$ matrix or a $2 \times 3$ matrix? Any comment is welcome.
3
votes
1answer
88 views

Co-ordinate axes: What does the $e$ in ${\hat e}_x$ stand for?

In vector analysis for $\mathbb{R^3}$ we write standard basis vectors in various forms like $\{\hat{x}, \hat{y}, \hat{z} \}$, $\{ \hat{\imath}, \hat{\jmath}, \hat{k}\}$, $\{ {\hat e}_x, {\hat e}_y, ...
7
votes
2answers
149 views

Literature on general paradox?

I suppose this one teeters on the edge of un-mathematical, but here it goes... I've been on something of a logic binge lately and have (surprise, surprise!) especially been interested in the results ...
5
votes
1answer
253 views

looking for materials on Martin Axiom

Recently, I am learning the Kunen's set theory. Now I will reach the second part of the book, i.e., the important Martin Axiom is introduced here. I found it is a little complex and difficult for a ...
3
votes
2answers
206 views

Determining distribution of $X_t = \int_0^t W_s^2 \mathrm{d} s$

Premise Let $W_t$ be the standard Wiener process, and let $X_t = \int_0^t W_s^2 \mathrm{d} s$. I am interested in determining the distribution of $X_t$. What I did My line of attack has been to ...
4
votes
2answers
2k views

How is a singular continuous measure defined?

On a measurable space, how is a measure being singular continuous relative to another defined? I searched on the internet and in some books to no avail and it mostly appears in a special case - the ...
29
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28answers
4k views

Classical texts that should not be missing from any shelf [closed]

It seems to me as if many modern texts are rather streamlined. They are designed not to expect too much from the reader but they often miss the depth of respective classical literature. The purpose ...
1
vote
1answer
147 views

Need reference about quadratic forms on abelian groups.

Let $B$ and $C$ be abelian groups (in additive notation). We call a function $f:B\rightarrow C$ a quadratic form if for all $x,y,z \in B$, the function $f$ satisfies the relation ...
3
votes
1answer
1k views

Looking for a beginner to advanced maths series

I asked this question previously, but guess I didnt make clear what I am looking for (or something) I am looking for a series of books, like a full set highschool maths curriculum, just to refresh ...
2
votes
2answers
377 views

Primitive roots of odd primes

The following facts about primitive roots of an odd prime seem to be well known. For example, they both appear as exercises in Burton's Elementary Number Theory. Let $p$ be an odd prime. Then: ...
2
votes
1answer
163 views

cumulants and infinite divisibility

Where might I find a clear exposition of how to prove that a real-valued probability distribution for which all moments exist is infinitely divisible if and only if all of its cumulants of even order ...
27
votes
2answers
2k views

Original works of great mathematician Évariste Galois

Through this question I wanted to know the original works of Galois. When I was reading Galois theory ( since from last month ) , I have been seeing one common line in every book, whose essence ...
8
votes
3answers
3k views

Difficulties with Chapter 2 in Rudin

I have been reading Rudin (Principles of Mathematical Analysis) on my own now for around a month or so. While I was able to complete the first chapter without any difficulty, I am having problems ...
1
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0answers
64 views

reference request

Can anybody help me to find the books on numerical solutions of partial differential equations including examples on irregular geometry (specially books or links on matlab code examples in this case)? ...
1
vote
1answer
58 views

Anybody got a link for work done on metrics for rational functions?

I was just thinking that as rational functions form an ordered field you could describe analogous version of the absolute value function, but we don't quite have a 'metric' - for example |1/x| < e ...
8
votes
5answers
806 views

I want to study mathematics ahead of high school, but I found that I'm rusty on the elementary stuff

Next week, I'm beginning the 2nd semester of 9th grade in the country's leading Comp Sci High School. (the profile is actually Math-Comp Sci, but this HS focuses more on Comp Sci, whereas other ones ...
7
votes
3answers
434 views

Reference requests: Jitsuro Nagura

I spent some time today looking for any biographical information on Jitsuro Nagura and came up empty-handed. Any suggestions welcome. Also, the Wiki note on the Chebyshev $\psi$ function says that ...
2
votes
3answers
239 views

Intermediate growth rates

Is there any simple function/formula $f(n)$, which eventually dominates every $cn$ for every $c$, and is eventually dominated by $a \cdot n \cdot \ln^k(n)$ for every $a,k \in \mathbb{Z}$, where ...
10
votes
7answers
5k views

Any good Graduate Level linear algebra textbook for practice/problem solving?

I am looking for good graduate linear algebra books that contain practice problems with solutions (which is better) or hints to solve the problems. By the way, two graduate courses I am gonna take are ...
7
votes
5answers
3k views

Need Help: Any good textbook in undergrad multi-variable analysis/calculus?

This semester, I will be taking a senior undergrad course in advanced calculus "real analysis of several variables", and we will be covering topics like: -Differentiability. -Open mapping theorem. ...
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0answers
85 views

Reference Request: Elementary introduction to holomorphic induction's role in index theory

I am currently working on an index theory senior project which involves Dirac operators, spin modules and holomorphic induction on the representation ring Lie groups. My primary reference is ...
1
vote
1answer
88 views

Centralizers in reductive Liegroups = unimodular?

Let $G$ be a real reductive group. Why is the centralizer of an element unimodular? What is a reference?
4
votes
2answers
404 views

Turing's 1939 paper on ordinal logic

I am reading Turing's 1939 paper on ordinal logic ("Systems of Logic Based on Ordinals", A. M. Turing, Proc. London Math. Soc. ser. 2, 45 (1939), #1, 161-228, DOI: 10.1112/plms/s2-45.1.161.) ...
1
vote
1answer
354 views

Properties of generalized limits aka nets

I want to find some article or a book which contains all general properties of nets. Of course some of them similar to properties of sequences with almost the same proofs, but I don't fill the edge, ...